1. Testing the origin of high- energy cosmic rays
A.Vladimirov
G.Johannesson
IVM
T.Porter
Adriani+2011

2. Spectrum of cosmic rays
All particle CR spectrum is almost featureless:
the knee
the ankle
GZK cutoff
These were the only features in >12 decades in energy and >32 decades in intensity!
New break?
Galactic
Galactic+extragalactic
GZK cutoff
extragalactic

3. PAMELA: Proton and helium spectra vs. rigidity
Hardening
dip
break
rigidity
The same break rigidity for p and He ~240 GV
The spectrum becomes flatter above the break
Spectral softening near the break, the “dip”
The differences between p and He spectral indices Δ = δp - δHe are about the same below and above the break

4. PAMELA: p/He ratio break rigidity
The p/He ratio is smooth and does not have a feature at the break rigidity

5. p/He ratio (Blasi & Amato 2011)
Proposed a model where the difference between p and He spectral slopes is explained by fragmentation of He
Requires τfragm < τesc
Works only for Kolmogorov diffusion (δ ~1/3)
Requires fine tuning: grammage ×2, somewhat different D0
Required grammage is too large (excess B, pbars)
Does not take into account production of secondary 3He (data: total He = 3He+4He)
Overproduces secondary species
We ADOPT different injection spectra for p and Z>1 ad hoc

6. Rationale Scenario P: interstellar Propagation effects
Change in CR transport: D ~ ρδ, δ = 0.3/0.15 below/above the break
Scenario I(a): CR Injection effects, a source with spectral break
Breaks in the injection spectrum of CR sources
Scenario I(b): CR Injection effects, a composite source
Two types of CR sources (soft and hard) uniformly mixed in the Galaxy
Scenario H: local High energy source
Low energy CRs are produced by sources distributed in the Galaxy
High energy CRs are coming from a local source
Scenario L: local Low energy source (special case!)
High energy CRs are produced by sources distributed in the Galaxy
Low energy CRs are coming from a local source
No reacceleration, δ = 0.67 below/above the break
Scenario R: Reference model
Tuned to pre-PAMELA CR data
Calculations employ GALPROP Webrun:

7. Summary of model parameters
Propagation
Reference
Injection
Local sources
The values of propagation parameters are taken from the Bayesian analysis by Trotta+’2011 and slightly adjusted (except model L)

8. Diffusion coefficient
CR injection spectra and the diffusion coefficient in different scenarios
Injection spectra
Diffusion coefficient L
R, I
ρ2.2 q(ρ), a.u.
ρ2.2 q(ρ), a.u.
D(ρ)/β, 1028 cm-2 s-1
P, H
Rigidity ρ, GV
Rigidity ρ, GV
Propagation: stochastic reacceleration model, except scenario L
Injection spectra adjusted to match the CR p and He spectra

9. P and He spectra in different scenarios
Reference
P and He spectra in different scenarios
All scenarios are tuned to the data, except the Reference scenario
Scenarios L and H: the local source component is calculated by the subtraction of the propagated Galactic spectrum from the data
The local source is assumed to be close to us, so no propagation; only primary CR species R
Propagation
Injection P I
Local LE
Local HE L H

10. B/C ratio in different scenarios
Reference
B/C ratio in different scenarios
All scenarios reproduce B/C below ~300 GeV/nucleon
Above 300 GeV/nucleon B/C is flatter in Scenario P
Local sources are assumed to produce only primary isotopes
B/C is steeper in scenario L and H, but due to the different reasons
Scenario L: P-L index of the diffusion coefficient steepens to 0.67
Scenario H: there is no Boron in the local source, but there is Carbon
Propagation
Injection
Local LE
Local HE

11. Antiprotons and pbar/p ratio in different scenarios
All scenarios are consistent with existing antiproton data (except scenario L)
Predict different behavior at HE

12. p/He ratio and CR anisotropy ratio in different scenarios
Ptuskin+’2006
The lower anisotropy figure illustrates the effect of local sources, but it depends on their assumed ages, distances, and the spectra of accelerated particles
Local sources

13. Mid-latitude diffuse emission in different scenarios
Reference
Mid-latitude diffuse emission in different scenarios
Propagation
Injection
All scenarios are consistent with the Fermi- LAT data
Predictions for π0-decay component at HE are different
Intensities of other components (IC, isotropic, sources) are comparable
Requires large statistics at HE to distinguish
Local LE
Local HE

15. Conclusions
There is no any single model capable to explain all observed features
The model predictions can be tested by current (e.g., AMS-2, CREAM) or near future experiments
Scenario P (interstellar propagation effects) is the favorite scenario, although other scenarios can’t be ruled out yet
Important issue is the reality of the “dip” feature, which can only be understood in Scenario L
Scenario L (plain diffusion model) seems to be ruled out on the base of pbar and anisotropy arguments
Submitted to ApJ (arXiv: )

17. Backup slides

18. Posterior probability distributions from Bayesian analysis (Trotta+’2011)
Normalization of the diffusion coeff. and its index
color bar – 68%, 95% error ranges
vertical line – posterior mean
✗ - the best fit
Reacceleration model (GALPROP)
δ = 0.3 – very close to classical value 1/3 for Kolmogorov diffusion
All parameters are very close to those derived by the “eye-fitting” method
Alfven speed Halo size
Injection index below/above the 1 GV

19. CRs in the Interstellar Medium
42 sigma ( data)
HESS
SNR RX J
PSF
ISM
Chandra
X,γ
HESS e
synchrotron B IC
Fermi P He
CNO
ISRF
•diffusion
•energy losses
•diffusive reacceleration
•convection
•production of
secondaries
bremss
WIMP
annihil.
gas P _ π P,
X,γ e + - π + - e
gas
solar modulation P _ π + - p
LiBeB
Flux He
CNO e
20 GeV/n
BESS
CR species:
Only 1 location
modulation
ACE
PAMELA
helio-modulation

20. Secondary/primary nuclei ratio & CR propagation
Typical parameters (model-dependent):
D ~ 1028 (ρ/1 GV)α cm2/s
α ≈
Zh ~ 4-6 kpc; VA ~ 30 km/s
Be10/Be9
Interstellar
Zh increase
Using secondary/primary nuclei ratio (B/C) & radioactive isotopes (e.g. Be10):
Diffusion coefficient and its index
Galactic halo size Zh
Propagation mode and its parameters (e.g., reacceleration VA, convection Vz)
Propagation parameters are model-dependent

22. The Likelihood Function
Θ – a set of model parameters
ϕ = {ϕ1, ϕ2, ϕ3, ϕ4} – a set of modulation potentials; the number of modulation potentials corresponds to the number of data sets (experiments)
ΦX(Ei, Θ,ϕ) – the computed spectrum for CR species X
ΦXij – the measured spectrum (i runs through the data points for each experiment j)
σij – reported standard deviations
τj – error rescaling parameters
The full likelihood for all 5 experimental data sets:
– assuming that individual energy bins are independent

23. Sampling algorithm
SuperBayeS code (SUpersymmetry Parameters Extraction Routines for Bayesian Statistics, Ruiz de Austri+’06, Trotta+’08):
Markov Chain Monte Carlo methods
Nested sampling algorithm by John Skilling’04,06 and MultiNest by Feroz&Hobson’08
Computational effort ~13 CPU years, ~1.4×105 samples
Fit a total of 76 data points, 16 parameters, best fit chi-squared/dof ~ 1
Posterior mean <Θ> ≈ M-1 Σi=0…M-1 Θ(i)

24. Input parameters and prior ranges

25. 2D posterior probability distributions
Contours enclose 68% and 95% probability regions
- best fit
- posterior mean

26. Nuisance parameters Color bar – 68%, 95% error ranges
Vertical line – posterior mean
✗ – best fit
∨- prior value (as reported by experiments)

27. Summary of constraints on all parameters